The true quantum face of the “exponential” decay: Unstable systems in rest and in motion

K Urbanowski

doi:10.1051/epjconf/201716401032

Abstract

Results of theoretical studies and numerical calculations presented in the literature suggest that the survival probability P 0 (t ) has the exponential form starting from times much smaller than the lifetime τ up to times t ⪢τ and that P 0 (t ) exhibits inverse power–law behavior at the late time region for times longer than the so–called crossover time T ⪢ τ (The crossover time T is the time when the late time deviations of P 0 (t ) from the exponential form begin to dominate). More detailed analysis of the problem shows that in fact the survival probability P 0 (t ) can not take the pure exponential form at any time interval including times smaller than the lifetime τ or of the order of τ and it has has an oscillating form. We also study the survival probability of moving relativistic unstable particles with definite momentum p→≠0. These studies show that late time deviations of the survival probability of these particles from the exponential–like form of the decay law, that is the transition times region between exponential–like and non-exponential form of the survival probability, should occur much earlier than it follows from the classical standard considerations.

Highlights

EPJ Web of Conferences 164, 01032 (2017)EPJ Web of Conferences initial stage of the decay process
The experimental confirmation of this effect was reported, e.g. in [11] and recently in [12]. All these results of theoretical and experimental researches caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time, exponential, and late time having inverse–power law form [13]
This belief is reinforced by a numerous presentations in the literature decay curves obtained for quantum models of unstable systems

Summary

Introduction

Initial stage of the decay process (see [6] and references therein). Theoretical analysis shows that at late times the survival probability (i. e. the decay law) should tends to zero as t → ∞ much more slowly than any exponential function of time and that as function of time it has the inverse power–like form at this regime of time [5, 6]. The experimental confirmation of this effect was reported, e.g. in [11] and recently in [12] All these results of theoretical and experimental researches caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial), exponential (or "canonical"), and late time having inverse–power law form [13]. This belief is reinforced by a numerous presentations in the literature decay curves obtained for quantum models of unstable systems. Our results shows that conclusions relating to the quantum decay processes of moving particles based on the use of the classical physics time dilation relation need not be universally valid

Preliminaries

The Breit–Wigner model

Moving unstable systems with constant momentum

Summary